Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61071 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C79 · Schur multiplier (H2) = C28 |
| direct product | C79×#61274 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C79 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C79 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C79 ◁ #525×C79 ◁ G | |
1824 conjugacy classes of subgroups.
| minimal degree | μ(G) = 103 |
| transitive degree | μt(G) = 5056 |
A minimal faithful permutation representation — 5 generators on 103 points:
(1,2,5,4)(3,7,8,6)(9,10,14,13)(11,19,21,24)(12,17,18,15)(16,23,20,22)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103);(1,3)(2,6)(4,7)(5,8)(10,13)(12,18)(16,20)(19,24);(1,4,5,2)(3,7,8,6)(9,11,14,21)(10,16,13,20)(12,19,18,24)(15,23,17,22);(3,8)(6,7)(9,12,14,18)(10,17,13,15)(11,19,21,24)(16,22,20,23);(9,13)(10,14)(11,20)(12,15)(16,21)(17,18)(19,23)(22,24)4345 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 54262);